To achieve fast and high-accuracy detection with single-photon light detection and ranging（LiDAR), this paper designs a high-flux and high-repetition-rate single-photon LiDAR system and proposes a waveform correction method tailored for this system. By increasing the photon counting rate, the system significantly reduces the single-pixel acquisition time. Meanwhile, the waveform correction method effectively addresses the issues of waveform distortion caused by the dead time of single-photon detectors under high-flux and high-repetition-rate conditions, thereby enhancing the inversion accuracy of target signal strength and depth. The system employs a free-running single-photon detector in the near-infrared band with a dead time of 1 200 ns and a laser repetition rate of 3 MHz, and the single-pixel acquisition time is set to 1 ms. Simulation and experimental results demonstrate that the proposed method achieves a distance inversion accuracy of 4.9 mm and a photon flux inversion accuracy of 0.16 photons. In the 3D imaging experiment, using a 50 × 50 point-to-point scanning pattern, the imaging plane fitting accuracy reaches 8 mm, enabling high-precision 3D imaging of small UAVs at close range. This study provides a new technical approach for the application of single-photon LiDAR in fast imaging fields such as target detection and resource mapping.